| In this dissertation, we present several methodologies for mining spatial and time-sequence data obtained in diverse domains. We first propose a new spatial randomness test and classification method for binary spatial data with specific application to the detection and identification of spatial defect patterns on semiconductor wafer maps. We present the generalized join-count (JC)-based statistic as an alternative approach, and derive a procedure to determine the optimal weights of JC-based statistics. In the proposed methodology, a spatial correlogram, which transforms binary spatial data into time-sequence data, is used as a novel feature to detect spatial autocorrelation and classify spatial defect patterns on the wafer maps.;Secondly, we propose a novel distance measure, denoted weighted dynamic time warping (WDTW), for time series classification and clustering problems. The dynamic time warping (DTW) algorithm has been extensively used as a distance measure in combination with the distance-based classifiers. However, the DTW algorithm ignores the relative importance of the phase distance between points in a time series, possibly leading to misclassification. Therefore, we propose a WDTW distance measure which does account for the relative importance of each point in terms of the phase distance between the time series points.;Thirdly, we propose a wavelet-based anomaly detection procedure to detect any possible process fault with time-sequence data that have some local variations even under normal working conditions. To handle the large number of parameters in both the mean and variance models, we have developed the wavelet-based mean and variance thresholding procedure to extract a few important wavelet coefficients that may explain local variations in the time domain.;Finally, we propose a kernel-based regression with lagged dependent variables. Kernel-based regression techniques are extensively used for exploring the nonlinearity of data in a relatively easy procedure involving the use of various kernel functions. However, the major drawback of current kernel-based regression techniques is their underlying assumption that there is no autocorrelation in the residuals of observations. To avoid this problem, we propose a kernel-based regression model with lagged dependent variables (LDVs), considering autocorrelations of both the response variables and the nonlinearity of data. |
